On the space of ultradistributions vanishing at infinity

We study the structural and linear topological properties of the space B˙ω′∗ of ultradistributions vanishing at infinity (with respect to a weight function ω). Particularly, we show the first structure theorem for B˙ω′∗ under weaker hypotheses than were known so far. As an application, we determine the structure of the S-asymptotic behavior of ultradistributions.